Electric power systems (grids) are comprised of generating stations or power plants, transmission and distribution lines interconnected into networks, a variety of loads, and many other necessary pieces of equipment. Electrical power systems' operation and control functions rely on analytical software tools (computer programs) for setting safe and secure operating limits and maintaining reliable service. These software tools utilize mathematical models of the power system components and equipment in the form of differential and algebraic equations. The mathematical models, in conjunction with ohm's, Kirchhoff's, and other physical laws, are utilized to assemble sets of equations encoded into computer programs or software tools that represent the behavior of the power grid. The software tools provide the solutions to the above mentioned sets of equations and therefore are essential to the operation and control of power systems. The software tools can be coded or programmed in any and all programming languages and these programs can run on any and all computer hardware platforms with their associated operating systems. The power system operator at a typical energy control center utilizes these software tools or computer programs on a continuous basis for operating the power grid. These tools inform the power system operators of the state (voltage magnitude and phase-angle at all the buses) of the power grid so that they can take action to ensure that all system voltages and power flows are within specified limits and the system can survive potential disturbances. These software tools are heavily relied upon for monitoring and managing the performance of power systems. They are also essential to automating various facets of power systems' operations and control.
The continuously utilized or on-line software tools are deployed for real-time operation and control of power systems at utility or Independent System Operator (ISO) or Regional Transmission Operator (RTO) energy control centers. These software tools typically require telemetered data from voltage, current and power measurement devices throughout the power grid. The data is collected via “supervisory control and data acquisition” (SCADA) or similar systems. A SCADA system and the associated computational tools are collectively referred to as an Energy Management System (EMS). The collected asynchronous (scanned every 2 to 4 seconds) telemetry data from SCADA is fed into an existing software tool, here referred to as a traditional State Estimator (SE). Given these measurements, the SE estimates the state of the power system using typically a Least-Squares best-fit procedure. The SE output or the state of the power system is in turn used to determine the resulting power flow values as well as the system parameters that are not directly measured or measurable. Other advanced network analysis functions such as operator's power flow, contingency ranking and analysis, economic dispatch, etc., may also be implemented using the state of the system or the SE output.
The AC state estimation problem formulation in the SE software tool results in a set of nonlinear equations. In a traditional SE tool, Newton and Newton-Raphson methods or variations thereof are conventionally used to iteratively find solutions to the set of nonlinear equations. Newton-based iterative solution methods, for example, begin with an initial estimate (guess) of the solution where a matrix of gradients or partial derivatives, referred to as “the Jacobian,” may be determined. This matrix is used to determine a correction to the initial estimate using a linear approximation of the nonlinear equations. The correction is then added to the initial estimate, which is then used as a new solution or starting point in the iterative process. Iterations are continued until the difference between two consecutive solutions is less than a specified tolerance, i.e., a convergence criterion is satisfied or convergence is achieved. Newton-based solution methods normally converge in a few iterations; however, these methods require that the initial estimate be close to the true or actual solution.
The prior art related to the traditional SE tool described above thus depends on iterative solution of a set of nonlinear equations and therefore on the quality of the initial estimate (guess). If the initial estimate is far away from the solution point of the problem, due to sudden changes or dynamic system fluctuations, non-convergence may result, leaving the power grid operator blind to the state of the system. Hence, this divergence can therefore limit the use of iterative solutions in the real-time and dynamic determination of the state of the power system, especially when severe disturbances occur in the system.
The new art presented via the disclosure herein provides a more robust software tool for operation and control of power grids by solving the sets of nonlinear equations non-iteratively and in one shot for determining the state of the power system. There is no initial estimate or guess required therefore eliminating this dependency. There are no iterations and therefore no divergence issues. Such software tools provide a superior, more robust, and more reliable performance in the operation and control of power grids. The new software tools disclosed herein are envisioned to be an integral part of a new generation of the SCADA/EMS to be developed and deployed.